Easy avg velocity problem I can't figure out

[weeeee123]

Homework Statement

First half of a trip is @ 10 MPH
Second half of a trip is @ 40 MPH
Avg velocity?

Homework Equations

(Vi+Vf)/2 = avg velocity...?

The Attempt at a Solution

K, this is obviously a simple question but for some reason when I do it I get it wrong, and I'm 100% sure I'm right. But I'm not. WTH?

I know the answer is 16, because the answer is given to me. I don't know how to get to there though for whatever reason. What I did was basically weight each velocity by multiplying each by .5 since each speed is for half the time. I get 25, which is wrong. Then I thought about it this way. If I go 10 MPH for half an hour, that's 5 miles. Then if I go 40 MPH for half an hour, that's 20 miles. In total I went 25 miles in one hour, and my avg velocity should be 25 in that case. What am I missing?

 

[berkeman]

Homework Statement

First half of a trip is @ 10 MPH
Second half of a trip is @ 40 MPH
Avg velocity?

Homework Equations

(Vi+Vf)/2 = avg velocity...?

The Attempt at a Solution

K, this is obviously a simple question but for some reason when I do it I get it wrong, and I'm 100% sure I'm right. But I'm not. WTH?

I know the answer is 16, because the answer is given to me. I don't know how to get to there though for whatever reason. What I did was basically weight each velocity by multiplying each by .5 since each speed is for half the time. I get 25, which is wrong. Then I thought about it this way. If I go 10 MPH for half an hour, that's 5 miles. Then if I go 40 MPH for half an hour, that's 20 miles. In total I went 25 miles in one hour, and my avg velocity should be 25 in that case. What am I missing?

The equation that you wrote for the average velocity is incorrect. Instead, the average velocity is the total distance divided by the total time. Try it that way instead.

(Don't worry -- this is a common error, and it's why they are asking you this question.)

 

[weeeee123]

I quite honestly didn't even use that equation. I basically did what you said, dividing the total distance traveled by the total time.

avg vel = (40 *.5t + 10 *.5t)/t
= t(40*.5 + 10 * .5)/t
= (40 * .5 + 10 * .5)
= 25

ummm...?

 

[berkeman]

I quite honestly didn't even use that equation. I basically did what you said, dividing the total distance traveled by the total time.

avg vel = (40 *.5t + 10 *.5t)/t
= t(40*.5 + 10 * .5)/t
= (40 * .5 + 10 * .5)
= 25

ummm...?

When they say "first half" and "second half" of the trip, they mean in distance, not in time...

 

[weeeee123]

When they say "first half" and "second half" of the trip, they mean in distance, not in time...

Oh wow hahahahaha thank you